SOLUTION: Debts of $400.00, $450.00 and $500.00 are due in one year, eighteen months and thirty months from now respectively. Determine the single payment now that would settle the debts

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Question 1118428: Debts of $400.00, $450.00 and $500.00 are due in one year, eighteen months and thirty months from now respectively.
Determine the single payment now that would settle the debts if interest is 8% p.a. compounded quarterly. Let the focal date be now.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
400 is due in one year = 12 months.
450 is due in 18 months.
500 is due in 30 months.

the interest rate is 8% per year compounded quarterly.

8% per year compounded quarterly is equal to 8/4 = 2% per quarter.

there are 4 quarters in a year.

since a year is equal to 12 months, then there are 4 quarters in 12 months which means there are 3 months in a quarter.

you need to translate everything to quarters.

1 year * 4 = 4 quarters.

18 months / 3 = 6 quarters.

30 months / 3 = 10 quarters.

note that 18 months divided by 12 = 1.5 years * 4 = 6 quarters.

note also that 30 months divided by 12 = 2.5 years * 4 = 10 quarters.

it all checks out.

400 is due in 1 year = 4 quarters.

the interest rate is .02 per quarter.

divide 400 by 1.02^4 to get a present value of 369.5381704.

450 is due in 18 months = 1.5 years = 6 quarters.

divide 450 by 1.02^6 to get a present value of 399.587122.

500 is due in 30 months = 2.5 years = 10 quarters.

divide 500 by 1.02^10 to get a present value of 410.1741499.

take the sum of all 3 present values to get a combined present value of 1179.299442.

that amount invested at 2% per quarter will cover all 3 payments.

this can be seen in the following excel spreadsheet printout.

$$$

if they paid 1179.299442 today, that would be the equivalent of making the payments at the time indicated in the problem.